{"id":"https://openalex.org/W2134765312","doi":"https://doi.org/10.1109/tit.2009.2030470","title":"On the Information Rate of MIMO Systems With Finite Rate Channel State Feedback Using Beamforming and Power On/Off Strategy","display_name":"On the Information Rate of MIMO Systems With Finite Rate Channel State Feedback Using Beamforming and Power On/Off Strategy","publication_year":2009,"publication_date":"2009-10-27","ids":{"openalex":"https://openalex.org/W2134765312","doi":"https://doi.org/10.1109/tit.2009.2030470","mag":"2134765312"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2009.2030470","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2009.2030470","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100752236","display_name":"Wei Dai","orcid":"https://orcid.org/0000-0002-4781-3485"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wei Dai","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, Urbana, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084454849","display_name":"Youjian Liu","orcid":"https://orcid.org/0000-0003-4681-0546"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Youjian Liu","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017012202","display_name":"Brian Rider","orcid":"https://orcid.org/0000-0002-0538-8441"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. Rider","raw_affiliation_strings":["Mathematics Department, University of Colorado, Boulder, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073153992","display_name":"Vincent K. N. Lau","orcid":"https://orcid.org/0000-0001-7769-6008"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"V.K.N. Lau","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong, China","institution_ids":["https://openalex.org/I200769079"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":2.4989,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.892827,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":100},"biblio":{"volume":"55","issue":"11","first_page":"5032","last_page":"5047"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.8199354410171509},{"id":"https://openalex.org/keywords/precoding","display_name":"Precoding","score":0.771024227142334},{"id":"https://openalex.org/keywords/channel-state-information","display_name":"Channel state information","score":0.7010552883148193},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.6042923927307129},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.46570947766304016},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45993518829345703},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.41879650950431824},{"id":"https://openalex.org/keywords/spectral-efficiency","display_name":"Spectral efficiency","score":0.41849592328071594},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40095964074134827},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3955625593662262},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3473963439464569},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.21071857213974},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.12722674012184143}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.8199354410171509},{"id":"https://openalex.org/C160562895","wikidata":"https://www.wikidata.org/wiki/Q7239557","display_name":"Precoding","level":4,"score":0.771024227142334},{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.7010552883148193},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.6042923927307129},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.46570947766304016},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45993518829345703},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.41879650950431824},{"id":"https://openalex.org/C137246740","wikidata":"https://www.wikidata.org/wiki/Q583970","display_name":"Spectral efficiency","level":3,"score":0.41849592328071594},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40095964074134827},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3955625593662262},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3473963439464569},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.21071857213974},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.12722674012184143},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2009.2030470","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2009.2030470","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.132.6813","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.132.6813","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ece.colorado.edu/~liue/publications/papers/Liu_ISIT05_on_off_feedback.pdf","raw_type":"text"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-18071","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-18071","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W174635644","https://openalex.org/W1488435683","https://openalex.org/W1561726166","https://openalex.org/W1563889663","https://openalex.org/W1969097180","https://openalex.org/W1991058183","https://openalex.org/W2009188663","https://openalex.org/W2027559193","https://openalex.org/W2035469609","https://openalex.org/W2074863717","https://openalex.org/W2099111195","https://openalex.org/W2100289761","https://openalex.org/W2104057862","https://openalex.org/W2104621895","https://openalex.org/W2106750175","https://openalex.org/W2108246702","https://openalex.org/W2109214279","https://openalex.org/W2115573600","https://openalex.org/W2117616158","https://openalex.org/W2120350343","https://openalex.org/W2120449325","https://openalex.org/W2123353262","https://openalex.org/W2123557425","https://openalex.org/W2124763586","https://openalex.org/W2125768494","https://openalex.org/W2127090918","https://openalex.org/W2130509920","https://openalex.org/W2130521103","https://openalex.org/W2132049438","https://openalex.org/W2133214726","https://openalex.org/W2136979582","https://openalex.org/W2139060658","https://openalex.org/W2147573094","https://openalex.org/W2149139492","https://openalex.org/W2149600388","https://openalex.org/W2151287068","https://openalex.org/W2151853371","https://openalex.org/W2152373327","https://openalex.org/W2158613296","https://openalex.org/W2161515500","https://openalex.org/W2162876202","https://openalex.org/W2165609888","https://openalex.org/W2169448252","https://openalex.org/W2170678594","https://openalex.org/W2181292907","https://openalex.org/W2952817145","https://openalex.org/W4242849907","https://openalex.org/W4293005804","https://openalex.org/W4362230038","https://openalex.org/W6607265895","https://openalex.org/W6633738730","https://openalex.org/W6647957881","https://openalex.org/W6678500933","https://openalex.org/W6679653658"],"related_works":["https://openalex.org/W2489379490","https://openalex.org/W2141031289","https://openalex.org/W2116541631","https://openalex.org/W2514205366","https://openalex.org/W3173074004","https://openalex.org/W2578955643","https://openalex.org/W1976511355","https://openalex.org/W2059045613","https://openalex.org/W2724724053","https://openalex.org/W1976249538"],"abstract_inverted_index":{"It":[0],"is":[1,22,29,36,46,123,191,197,209,247,255,262],"well":[2],"known":[3],"that":[4,33,120,138,147,251],"multiple-input":[5],"multiple-output":[6],"(MIMO)":[7],"systems":[8],"have":[9],"high":[10],"spectral":[11],"efficiency,":[12],"especially":[13],"when":[14,167],"channel":[15,143,194],"state":[16],"information":[17,66,245],"at":[18],"the":[19,34,51,58,64,89,93,97,102,108,112,139,142,148,151,159,168,185,201,206,218,227,232,243,252,259],"transmitter":[20],"(CSIT)":[21],"available.":[23],"In":[24,68],"many":[25],"practical":[26],"systems,":[27],"it":[28],"reasonable":[30],"to":[31,56,62,101,107,164,242],"assume":[32,137],"CSIT":[35],"obtained":[37],"by":[38,223],"a":[39,72,121,128,165,198,239],"limited":[40,59],"(i.e.,":[41],"finite":[42],"rate)":[43],"feedback":[44,60,207],"and":[45,83,106,145,158,172,215,237,258],"therefore":[47],"imperfect.":[48],"We":[49,134],"consider":[50],"design":[52],"problem":[53],"of":[54,92,96,154,161,170,187,193,200,220],"how":[55],"use":[57],"resource":[61],"maximize":[63],"achievable":[65,244],"rate.":[67],"particular,":[69],"we":[70,216],"develop":[71],"low":[73],"complexity":[74],"power":[75,116,181,235],"on/off":[76,117,182,236],"strategy":[77,118,183,254],"with":[78,127],"beamforming":[79,211,222],"(or":[80],"Grassmann":[81,228],"precoding),":[82],"analytically":[84],"characterize":[85,217],"its":[86],"performance.":[87],"Given":[88],"eigenvalue":[90],"decomposition":[91],"covariance":[94],"matrix":[95],"transmitted":[98],"signal,":[99],"refer":[100],"eigenvectors":[103],"as":[104,111],"beams,":[105],"corresponding":[109],"eigenvalues":[110],"beam's":[113],"power.":[114],"A":[115],"means":[119],"beam":[122],"either":[124],"turned":[125,132,156,189],"on":[126,157,190,226],"constant":[129,166],"power,":[130],"or":[131],"off.":[133],"will":[135],"first":[136],"beams":[140,155,188],"match":[141],"perfectly":[144],"show":[146,250],"ratio":[149,203],"between":[150],"optimal":[152,257],"number":[153,160,186],"antennas":[162,174],"converges":[163],"numbers":[169],"transmit":[171],"receive":[173],"approach":[175],"infinity":[176],"proportionally.":[177],"This":[178],"motivates":[179],"our":[180],"where":[184],"independent":[192],"realizations":[195],"but":[196],"function":[199],"signal-to-noise":[202],"(SNR).":[204],"When":[205],"rate":[208,246],"finite,":[210],"cannot":[212],"be":[213],"perfect,":[214],"effect":[219],"imperfect":[221],"quantization":[224],"bounds":[225],"manifold.":[229],"By":[230],"combining":[231],"results":[233],"for":[234,264],"beamforming,":[238],"good":[240],"approximation":[241,261],"derived.":[248],"Simulations":[249],"proposed":[253],"near":[256],"performance":[260],"accurate":[263],"all":[265],"experimented":[266],"SNRs.":[267]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":21},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}